Spin-2 Mesons in a Relativistic Hartree Description of Nuclei

Abstract

The role of the isovector spin-orbit potential in nuclear modeling has recently been explored in greater detail due largely in part to the PREX and CREX parity violating electron scattering (PVES) experiments. The result of both experiments have shown that the neutron-rich skins of $^{48}$Ca and $^{208}$Pb, as determined by the experimental analysis, are largely incompatible with current nuclear model predictions. One way to address, and potentially solve, this incompatibility has been to enhance the isovector spin-orbit sector of density functional models. Here, we explore the range of possible enhancements in the context of covariant density functional theory by introducing a new class of spin-2 \textit{massive} mesons to the Lagrangian. In doing so, we find that these mesons not only meaningfully contribute to the theory, but also mitigate problems seen in other works which enhance spin-orbit effects in finite nuclei. We also discuss the implications and future regarding this ``dilemma'' as it pertains to studies of nuclear forces and future experiments such as the Mainz Radius Experiment (MREX).

Figures (8)

• Figure 1: Point particle densities for protons (solid) and neutrons (dashed) in $^{48}$Ca (left) and $^{208}$Pb (right). We show the original RMFGO prediction without tensor mesons as a black line and the $\Delta$N$^2$LO$_{\rm GO}$ interaction which it was original fit in green. The effects of $\pm\Gamma_T$ can be seen best near the nuclear surface in $^{48}$Ca, near $\sim3$ fm.
• Figure 2: Same as in \ref{['fig:gammaT_ndens']} but for charge (solid) and minus weak (dashed) densities.
• Figure 3: Single particle energies for the different occupied shells in $^{48}$Ca for protons (left) and neutrons (right). The base RMFGO values are shown in the leftmost column as black bars and the effects of changing to $\pm\Gamma_T$ are shown as red and blue bars. Shell state names for each occupied level are shown on the right of each subfigure.
• Figure 4: Same as in \ref{['fig:gammaT_ndens']} but for changing $\Gamma_H$.
• Figure 5: Same as in \ref{['fig:gammaT-cdens']} but for changing $\Gamma_H$.